SOLUTION: Two planes leave simultaneously from the same airport, one flying due north and one flying due east. The northbound plane is flying 50 mph faster than the eastbound plane. After 3

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Question 487176: Two planes leave simultaneously from the same airport, one flying due north and one flying due east. The northbound plane is flying 50 mph faster than the eastbound plane. After 3 hours they are 2440 miles apart. Find the speed of each plane.
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
(3n-150)2+(3n)2=(2440)2
9n2-900n+22500+9n2=5953600
18n2-900n-5931100=0
9n2-450n-2965550=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 9x%5E2%2B-450x%2B-2965550+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-450%29%5E2-4%2A9%2A-2965550=106962300.

Discriminant d=106962300 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--450%2B-sqrt%28+106962300+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-450%29%2Bsqrt%28+106962300+%29%29%2F2%5C9+=+599.569887442386
x%5B2%5D+=+%28-%28-450%29-sqrt%28+106962300+%29%29%2F2%5C9+=+-549.569887442386

Quadratic expression 9x%5E2%2B-450x%2B-2965550 can be factored:
9x%5E2%2B-450x%2B-2965550+=+9%28x-599.569887442386%29%2A%28x--549.569887442386%29
Again, the answer is: 599.569887442386, -549.569887442386. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B-450%2Ax%2B-2965550+%29

Throwing out the negative answer, we get the speeds of the planes to be approximately 600 mph for the northbound plane, and 550 mph for the eastbound plane..